We present a new method for solving nonlinear integer arithmetic constraints. The method relies on the MCSat approach to solving nonlinear constraints, while using branch and bound in a conflict-directed manner. We report encouraging experimental results where the new procedure outperforms state-of-the-art SMT solvers based on bit-blasting.

The Multi-Story Space Assignment Problem (MSAP) is an innovative formulation of the multi-story facility assignment problem that allows one to model the location of departments of unequal size within multi-story facilities as a Generalized Quadratic 3-dimensional Assignment Problem (GQ3AP). Not only can the MSAP generate the design of the location of the departments in the facility, the MSAP al...

In this short paper we present a brief exposition of a composite decision process our unifying formulation of search procedures which provides new insights concerning the relationships among heuristic search, dynamic programming and branch and bound procedures.

Precise constraint satisfaction modeling requires specific knowledge acquired from multiple past cases. We address this issue with a general branch-and-bound algorithm that learns the parameters of a given global constraint from a small set of positive solutions. The idea is to cleverly explore the possible combinations taken by the constraint’s parameters without explicitly enumerating all com...

The problem of determining the largest order nd,k of a graph of maximum degree at most d and diameter at most k is well known as the degree/diameter problem. It is known that nd,k Md,k where Md,k is the Moore bound. For d = 4, the current best upper bound for n4,k is M4,k − 1. In this paper we study properties of graphs of order Md,k − 2 and we give a new upper bound for n4,k for k 3. © 2007 El...

The Maximum Agreement Forest problem has been extensively studied in phylogenetics. Most previous work is on two binary phylogenetic trees. In this paper, we study a generalized version of the problem: the Maximum Agreement Forest problem on multiple rooted multifurcating phylogenetic trees, from the perspective of fixed-parameter algorithms. By taking advantage of a new branch-and-bound strate...

We describe a new exact solver for the minimization of open stacks problem (MOSP). By combining nogood recording with a branch and bound strategy based on choosing which customer stack to close next, our solver is able to solve hard instances of MOSP some 5-6 orders of magnitude faster than the previous state of the art. We also derive several pruning schemes based on dominance relations which ...

We consider reoptimization (i.e., the solution of a problem based on information available from solving a similar problem) for branch-and-bound algorithms and propose a generic framework to construct a reoptimizing branch-and-bound algorithm. We apply this to an elevator scheduling algorithm solving similar subproblems to generate columns using branchand-bound. Our results indicate that reoptim...

A Bayesian probabilistic approach is presented for the damage detection of multistory frame structures. In this paper, a Bayesian probabilistic approach is applied to identify multiple damage locations using estimated modal parameters when (1) the measurement data are potentially corrupted with noise, (2) only a small number of degrees of freedom are measured, and (3) a few fundamental modes ar...